Q. 24.0( 4 Votes )

Differentiate log(1 + x2) with respect to tan–1x.

Answer :

Let u = log(1 + x2) and v = tan–1x.


We need to differentiate u with respect to v that is find.


On differentiating u with respect to x, we get



We know


[using chain rule]



However, and derivative of a constant is 0.





Now, on differentiating v with respect to x, we get



We know



We have





Thus,


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